How would I create this moving flowy mesh on a transparant mesh?
Extreme deformation meshes with blender tends to break the geometry of the mesh. Here I take a simple cube with 2 faces deleted and some twist modifiers. You animate by increasing the twist values.


Otherwise you could use a procedural texture on a sphere, you map it to an empty that has an animated position. Use alpha values to cut holes in the sphere mesh. Remember to make the inside traceable in Blender Internal, otherwise Cycles will do this automatically, allowing you to cast shadows inside.


And here is the example blend file I made these images with: